PreCalculus - Polar Curve Types

Learning Mode

Line

r = a/sin(θ) OR r = a/cos(θ); a ≠ 0

Circle

r = a*sin(θ) OR r = a*cos(θ); a > 0; r = a/2

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This set includes

Line

r = a/sin(θ) OR r = a/cos(θ); a ≠ 0

Circle

r = a*sin(θ) OR r = a*cos(θ); a > 0; r = a/2

Cardiod (Heart-shaped Limaçon)

r = a±b*sin(θ) OR r = a±b*cos(θ); a > 0, b > 0; a/b = 1

Inner Loop Limaçon

r = a±b*sin(θ) OR r = a±b*cos(θ); a > 0, b > 0; a/b < 1

Dimpled Limaçon

r = a±b*sin(θ) OR r = a±b*cos(θ); a > 0, b > 0; 1 < a/b < 2

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Regular Limaçon

r = a±b*sin(θ) OR r = a±b*cos(θ); a > 0, b > 0; a/b > 2

Rose Petal; n is even

r = a*sin(nθ) OR r = a*cos(nθ); a ≠ 0; 2n petals

Rose Petal; n is odd

r = a*sin(nθ) OR r = a*cos(nθ); a ≠ 0; n petals

Lemniscate

r^2 = a^2*sin(2θ) OR r^2 = a^2*cos(2θ); a ≠ 0